His side were 2-0 down after only 12 minutes, much to the annoyance of their new boss.
Ferguson said: "I told the players beforehand that the opening minutes were going to be vital because both sides were a bit low on confidence.
"If we started well I knew the home fans would become edgy. Instead, we handed Bristol the impetus and they have some good players who can knock it around after getting in front.
"You can't start games like that. But 90 minutes is not going to change my opinion and I believe I've inherited a sound squad who are just a bit low on belief at the moment.
"We had a good build-up to this game and I thought the players had taken a lot on board. But you have to transmit that into matches and it didn't happen."
Preston were caught cold after only 90 seconds when Paul Hartley's free-kick from the left reached Danny Haynes, who fired home first-time at the far post.
Another free-kick on 12 minutes, this time from Jamie McAllister caused mayhem again and after Nicky Maynard's shot was saved by Andy Lonergan, centre-back Liam Fontaine rifled home the rebound.
Chris Sedgwick's trickery got Preston back into the game on 27 minutes as he turned a defender inside out before crossing for Chris Brown to head home from six yards.
But more desperate defending at a free-kick 13 minutes into the second half saw Hartley's deep cross from the left reach Louis Carey and City's skipper looped a header over the diving Lonergan.
Substitute Evander Sno made it 4-1 with a low drive from the edge of the box shortly after coming on as an 88th-minute replacement and Ross Wallace's curling free-kick for North End in injury-time was only a consolation.
City manager Gary Johnson was relieved to celebrate his team's first home win since October and only their second victory in 11 Championship games.
"It was a real team performance," he said. "The difference was that we managed to get two goals ahead instead of trying to protect a single goal lead and that enabled the players to express themselves.
"It has been a difficult time for everyone at the club because there's been a fair amount of stick flying around for the team and myself as manager.
"But we are still right up there on the heels of the play-off contenders and if we can put a few wins back-to-back we will be in the thick of it again.
"If possible, I'd like to strengthen the squad before the end of the transfer window - but it's important people don't lose sight of the fact that we have a lot of talent here already."